Hyperbolic mean curvature flow

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

He, Chun-Lei²  Kong, De-Xing¹  Liu, Kefeng³ 

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[3] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

关键词: Hyperbolic mean curvature flow;    Extremal surface;    Short-time existence;    Nonlinear stability;   

DOI  :  10.1016/j.jde.2008.06.026

来源: Elsevier

【 摘 要 】

In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations is strictly hyperbolic, and based on this, we show that this flow admits a unique short-time smooth solution and possesses the nonlinear stability defined on the Euclidean space with dimension larger than 4. We derive nonlinear wave equations satisfied by some geometric quantities related to the hyperbolic mean curvature flow. Moreover, we also discuss the relation between the equations for hyperbolic mean curvature flow and the equations for extremal surfaces in the Minkowski space-time. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free